Cubic system special forms

There are 15 polyhedral forms in the cubic system. Most are Platonic or Catalan polyhedra (but not necessarily canonical) and 5 are unusual and appear in one or two of the cubic system classes

These are :

deltoid dodecahedron (aka rhombdodecahedron) in class 23
pentagonal dodecahedron(aka pyritohedron) in class m3 and 23
diakisdodecahedron (aka diploid) in class m3
pentagonal icositetrahedron (aka gyroid) in class 432
tetrahedral pentagonal dodecahedron(aka tetaroid) in class 23